2023 Fiscal Year Final Research Report
Scaling and proximity properties of discrete optimization
| Project/Area Number |
17K00037
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Keywords | 離散凸解析 / 最適化理論 / アルゴリズム |
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| Outline of Final Research Achievements |
The aim of this research is to construct a theoretical system for algorithm efficiency improvement based on scaling techniques for discrete optimisation, and to promote research with a view to applications of the theory. Scaling is a technique for improving efficiency by introducing a function approximation with a reduced scale, such as looking only at even points in the domain, and many successful examples are known in classical network flow and resource allocation problems.
In this study, we attempted to extend and build a theory for a wider class of discrete functions for which scaling techniques and proximity theorems have not been considered, and we made progress in clarifying the classes for which efficient algorithms can be constructed.
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| Free Research Field |
数理工学
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| Academic Significance and Societal Importance of the Research Achievements |
コンピュータ科学，オペレーションズ・リサーチ，経済学，ゲーム理論，数学などの様々な分野の研究者が，離散凸関数の概念に基づいた最適化において，スケーリング，近接性に関する議論がしやすくなり，効率的なアルゴリズムを用いることができるようになる．また整数計画の理論の応用や，一般的な数理最適化ソルバーの利用がしやすくなるという今後の展開も開けることが期待される．
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